On MSR Subspace Families of Lines
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A minimum storage regenerating (MSR) subspace family of 𝔽_q^2m is a set 𝒮 of m-spaces in 𝔽_q^2m such that for any m-space S in 𝒮 there exists an element in PGL(2m, q) which maps S to itself and fixes 𝒮∖{ S } pointwise. We show that an MSR subspace family of 2-spaces in 𝔽_q^4 has at most size 6 with equality if and only if it is a particular subset of a Segre variety. This implies that an (n, n-2, 4)-MSR code has n ≤ 9.
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